Related papers: Aspects of defects in integrable quantum field the…
That static electric and magnetic fields can store momentum may be perplexing, but is necessary to ensure total conservation of momentum. Simple situations in which such field momentum is transferred to nearby bodies and point charges have…
We discuss gravitational effects of global scalar fields and, especially, of global topological defects. We first give an introduction to the dynamics of global fields and the formation of defects. Next we investigate the induced…
We briefly review the concepts of generalized zero curvature conditions and integrability in higher dimensions, where integrability in this context is related to the existence of infinitely many conservation laws. Under certain assumptions,…
Impurity ions with orbitally degenerate ground electronic configuration embedded in metals are subjects to both the Kondo effect and the Jahn-Teller instability. While increasing the Jahn-Teller coupling, one passes, from the region of…
Covariant generalizations of well-known wave equations predict the existence of inertial-gravitational effects for a variety of quantum systems that range from Bose-Einstein condensates to particles in accelerators. Additional effects arise…
Many theories of modified gravity with higher order derivatives are usually ignored because of serious problems that appear due to an additional ghost degree of freedom. Most dangerously, it causes an immediate decay of the vacuum. However,…
Contrary to what is often stated, a fundamental spacetime discreteness need not contradict Lorentz invariance. A causal set's discreteness is in fact locally Lorentz invariant, and we recall the reasons why. For illustration, we introduce a…
These are lectures presented at the Les Houches Summer School ``Topology and Geometry in Physics'', July 1998. They provide a simple introduction to non perturbative methods of field theory in 1+1 dimensions, and their application to the…
In recent decades, the defect of finite extensions of valued fields has emerged as the main obstacle in several fundamental problems in algebraic geometry such as the local uniformization problem. Hence, it is important to identify…
We study integrable deformations of sine-Liouville conformal field theory. Every integrable perturbation of this model is related to the series of quantum integrals of motion (hierarchy). We construct the factorized scattering matrices for…
When it comes to performing thought experiments with black holes, Einstein-Bohr like discussions have to be re-opened. For instance one can ask what happens to the quantum state of a black hole when the wave function of a single ingoing…
In this contribution, some solutions of the Klein-Gordon equation in the G\"odel-type metrics with an embedded cosmic string are considered. The quantum dynamics of a scalar particle in three spaces whose metric is described by different…
We explore various combinatorial problems mostly borrowed from physics, that share the property of being continuously or discretely integrable, a feature that guarantees the existence of conservation laws that often make the problems…
Topological defects play a fundamental role in the investigation of symmetries in quantum field theories. For conformal field theories in two space-time dimensions, it is possible to construct these defects using lattice models allowing…
We study various aspects of codimension one defects in free scalar field theory, with particular emphasis on line defects in two-dimensions. These defects are generically non-conformal, but include conformal and topological defects as…
The concept of discrepancy plays an important role in the study of uniformity properties of point sets. For sets of random points, the discrepancy is a random variable. We apply techniques from quantum field theory to translate the problem…
A (very) brief review of topological defects and their possible cosmic roles. I emphasize in particular that superheavy defects needed for structure formation can peacefully coexist with inflation, despite the claims to the contrary which…
Following our attempts to define quasi-integrability in which we related this concept to a particular symmetry of the two-soliton function we check this condition in three classes of modified Sine-Gordon models in (1+1) dimensions. We find…
A Lagrangian approach is proposed and developed to study defects within affine Toda field theories. In particular, a suitable Lax pair is constructed together with examples of conserved charges. It is found that only those models based on…
Some formulae for the perturbations of the matter fields are summarized within the framework of the second-order gauge-invariant cosmological perturbation theory in a four dimensional homogeneous isotropic universe, which is developed in…